Abstract
Previous analysis of the Jacobi-matrix method based on the underlying SO(2,1) Lie algebra is extended to the Coulomb Hamiltonian in parabolic coordinates. The general solution of the generic SO(2,1) eigenvalue equation is constructed and special cases, which furnish expansions of the Coulomb functions ψ(±)k(r) in a complete set of parabolic Sturmians, are discussed.